Sketch out utility = 30 and utility = 60 indifference curves for each of the following utility functions. In each case describe the type of preferences that appear to be represented by each utility function:

a. U(x, y) = 2 ∗ x + y

b. U(x, y) = 10 + x + y

c. U(x, y) = 3 ∗ x ∗ y

d. U(x, y) = Minimum (3 ∗ x, y)